A Conversation with Walter T. Federer - A. S. Hedayat
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Statistical Science
2005, Vol. 20, No. 3, 302–315
DOI 10.1214/088342305000000142
© Institute of Mathematical Statistics, 2005
A Conversation with Walter T. Federer
A. S. Hedayat
Abstract. Walter Theodore Federer was born on August 23, 1915 in
Cheyenne, Wyoming. He received a B.S. in agronomy from Colorado State
University in 1939. In 1941 he received the M.S. degree in plant breed-
ing from Kansas State University. His Ph.D. in mathematical statistics from
Iowa State University was awarded in 1948. He held the position of Associate
Geneticist while working on the Guayule Research Project, USDA, in Sali-
nas, California. While completing his Ph.D. at Iowa State University, he was
Associate Statistician in the Agricultural Marketing Service in Ames, Iowa.
His next position was as Professor of Biological Statistics in the College of
Agricultural and Life Sciences at Cornell University. He was also the Admin-
istrator of the Biometrics Unit in the Department of Plant Breeding. He was
awarded the Liberty Hyde Bailey Professor of Statistics Chair in 1978, which
he held until retirement in 1986, since which he has had emeritus status.
Dr. Federer was Secretary and Program Coordinator for the Eastern North
American Region (ENAR) of the International Biometric Society from 1950
to 1953, President-Elect of ENAR in 1959 and President in 1960. He was
Chairman and Executive Secretary of the Committee of Presidents of Statisti-
cal Societies (1965–1972), Book Reviews Editor (1964–1972) and Associate
Editor for Biometrics (1972–1976), Associate Editor for Communications
in Statistics (1972–1994) and Associate Editor for the Journal of Statistical
Planning and Inference (1976–1990). He was a member of national, inter-
national, university and government panels and boards, and was a consultant
for several international research stations.
Dr. Federer is a Fellow of the American Statistical Association (1958),
American Association for the Advancement of Science (1962), Royal Statis-
tical Society (1964) and the Institute of Mathematical Statistics (1967), and
was elected a Member of the International Statistical Institute (1974). He was
awarded the Honor Alumnus Achievement Award (1972) and Honored
Alumnus Award (2001) by Colorado State University, and the Distinguished
Service in Agriculture Award (1988) by Kansas State University.
This conversation took place in April 2002 at Uni- PERSONAL
versity of Illinois at Chicago when Federer was in- Hedayat: Do you want to share with us any as-
vited to the Department of Mathematics, Statistics and pects of your family life?
Computer Science to present a lecture entitled “Frac- Federer: I had the most wonderful parents in
tional Combinatorials.” This interview was partially the world. They fashioned my principles and way
conducted via e-mail. of life. My father homesteaded north of Cheyenne,
Wyoming. We moved to another small ranch when
I was four years old. My mother immigrated from
A. S. Hedayat is Distinguished Professor, Department Czechoslovakia when she was eight years old. We were
of Mathematics, Statistics and Computer Science, Uni- poor but came through the Great Depression in fine
versity of Illinois, Chicago, Illinois 60607-7045, USA style. There was only one thing I could fault my par-
(e-mail: hedayat@uic.edu). ents on and that was that they did not teach any of their
302A CONVERSATION WITH WALTER T. FEDERER 303
Sydney. My son and I visited several countries in Eu-
rope and traveled to India, Nepal and Sri Lanka. I also
visited the International Rice Research Institute in the
Philippines. These years away from Ithaca were very
much enjoyed by the family.
I first met my second wife, Edna Hammond Morusty,
in September 1979. Guess where: square dancing. We
were married in March 1982. This has been a truly
wonderful marriage in that I have a talented and lovely
wife, a great travel companion, and obtained three
lovely, talented and beautiful stepdaughters. We trav-
eled to many countries: Brazil, Argentina and Peru in
1980, Italy, France and England in 1982, Venezuela in
1983, and Australia in 1984 (Sydney) and 1988 (Bris-
bane). We toured Egypt, Kenya and South Africa in
1989, Austria and Germany in 1990, and San Fran-
cisco, San Diego and Tijuana, Mexico in 1993 with
our second daughter, Suzanne. We traveled to Spain
with our oldest daughter, Sandra, in 1992, visiting sev-
eral museums, the World Trade Exposition and sev-
eral cities. Daughters Lynn, the youngest, and Suzanne
went with us to Sydney and Brisbane, Australia and
F IG . 1. Walt Federer in 2002. Beijing, China, in 1995. In 1996, Edna and I went
to the Netherlands where we met our granddaugh-
12 children to speak a foreign language. Mother could ter Robyn, a Rotary exchange student, in Amsterdam.
converse in at least seven languages. Father was flu- From there we went to Paris before returning to the
ent in German and could converse in the Scandinavian U.S. In 1997, we traveled to the International Maize
languages as he grew up in a German community in and Wheat Improvement Center (CIMMYT) in Mex-
Central Illinois. Forty-four languages were spoken in ico with daughter Suzanne. In 1998, I worked with
homes in Cheyenne and of course many people had Kaye E. Basford at the University of Queensland in
definite accents. Our parents did not want us to have Brisbane. Two overseas trips were made in 1999 with
an accent. I certainly could have used the German in Edna and daughter Suzanne: one to the International
college as Iowa State University required reading pro- Center for Agricultural Research in the Dry Land Ar-
ficiency in German and French for the Ph.D.! Growing eas (ICARDA), Aleppo, Syria, and one to Helsinki,
up in a large and congenial family was a very reward- Finland, for the ISI Meetings with side trips to St. Pe-
ing experience. tersburg, Russia, Tallinn, Estonia and Stockholm, Swe-
I was married to Lillian Elizabeth Vasey in 1945. den. In 2000, we with Suzanne made another trip to
She was a top-rated teacher of second grade in the CIMMYT in Mexico and to Colima University in Col-
Ames, Iowa, school system. We came to Ithaca in Au- ima on the Pacific Ocean side of Mexico. All of the
gust 1948, adopted a son Arthur John in 1954 and built trips were in connection with meetings, joint work
a house in 1956. Lillian and I had a great marriage until and/or lecturing, so they were mostly work trips for me,
her death in February 1978 from arteriosclerosis of the but my family was able to travel “around the world”
heart. We drove to Iowa and Wyoming about 20 times with me. Edna and I do enjoy our church and plays,
and to the West Coast and Canada several times. especially musicals. Edna takes two ballet classes and
We spent one sabbatical year, 1954–1955, in Hawaii one tap-dancing class and teaches these classes when
with the Hawaiian Sugar Planters Association and the instructor is not present. We do enjoy our 12 grand-
the Pineapple Research Institute. Our 1962–1963 and children and 14 great-grandchildren. Most live rela-
1969–1970 sabbatical years were spent in Madison, tively close to us in New York and so we do a bit of
Wisconsin, with the Mathematical Research Center at grandparenting. A wonderful family and home envi-
the University of Wisconsin. The 1977–1978 sabbati- ronment can’t do anything but be helpful to one’s pro-
cal was spent in Sydney, Australia, at the University of fessional life. We are strongly rooted in the Christian304 A. S. HEDAYAT
faith and this is a tremendous asset to a healthy, happy Dr. Powers gave me freedom to design my own ex-
and successful professional life. periments on guayule, even a cubic lattice experiment
design with 729 entries. All of these experiences in-
BECOMING A STATISTICIAN creased my interest in statistics, especially the design
Hedayat: How did you become interested in sta- and analysis aspects.
tistics?
Federer: Prior to entering college, I worked at the DAYS AT IOWA STATE UNIVERSITY
Cheyenne Horticultural Research Station in Cheyenne, Hedayat: When did you arrive at Iowa State and
Wyoming. The idea of planning and design of experi- who are some of the professors with whom you had
ments and summarizing the results became implanted contact?
in my mind without knowing anything about statis- Federer: During my stay at ISU in 1941–1942 and
tics, the subject. Dr. LeRoy Powers, geneticist and 1944–1948, I had the great fortune of taking courses
plant breeder, had considerable influence on me in this from, associating with and/or working with such in-
area. I was in the college preparatory division in high dividuals as Arnold J. King, George W. Snedecor,
school and hence took all the mathematics courses. William G. Cochran, Gertrude M. Cox, Alexander M.
Upon enrolling at Colorado State College (later Uni- Mood, George Brown, Oscar Kempthorne, Raymond J.
versity) in the fall of 1935, I entered as a major in Jensen, Earl E. Houseman, Morris Hansen, William
forestry, changed to unclassified and then to botany
Herwitz, Paul Homeyer, Theodore A. Bancroft,
for my sophomore year. Also, I enrolled in several
W. J. Youden, Daniel DeLury, Gerhardt Tintner, Mary
mathematics courses. In my junior year, my major was
Clem, George F. Sprague, Jay Lush, Dean Lindstrom
changed to agronomy and I was under the guidance of
and Ivar Johnson. This group of statisticians and
Professor Warren E. Leonard who taught a plot tech-
biologists contributed immensely to my statistical ed-
nique course that included experimental design and
ucation. I wrote papers with several of these individ-
analysis. In my senior year, I had a mathematical sta-
uals, some of which were published. T. A. Bancroft
tistics course under Professor Andrew G. Clark using a
and I wrote a lengthy unpublished monograph on ap-
book by Kinney. Acting upon the advice of Professor
plications of chi-squared. A. M. Mood and I wrote an
Leonard, I went to Kansas State University (KSU) to
do a Masters degree in plant breeding. From my two unpublished paper on indices of diversity. Many of the
statistics courses at Colorado State University (CSU), statistical results in survey and sampling theory and
it appeared that I was one of the most knowledgeable methodology well known to members of the Iowa State
individuals in statistics at KSU and consequently did a Statistical Laboratory in the forties appeared in publi-
lot of statistical consulting. Upon completing my M.S. cations in the fifties by individuals not connected with
degree, Arnold J. King offered me an assistantship in ISU. Much of this knowledge was taken as folklore at
the statistical laboratory of Iowa State University (ISU) Iowa State.
even though my major was in plant breeding. Dur- I have many pleasant memories of associations
ing my first quarter at ISU, I contacted William G. with graduate students at Iowa State. Some of my
Cochran and requested a change in my major from contemporaries were Lee Crump, Clifford Maloney,
plant breeding to statistics. He was agreeable but told Joe Dodson, George Darroch, Donovan Thompson,
me the change would most likely delay my receiving Daniel Horvitz, Garnet Macreary, Virgil Anderson,
the Ph.D. by a couple of years. That was okay with me Juliette Perotti, Helen Bozivich, Richard E. Atkins,
and I entered the statistical degree program at ISU in C. R. Weber, Kenneth Keller and others. These indi-
the fall of 1941. Pearl Harbor intervened and in May viduals helped to make classes, seminars and research
1942, I went to work with Dr. LeRoy Powers on the topics more interesting and educational.
Guayule Research Project, located in Salinas, Califor- Hedayat: Do you remember your Ph.D. qualifying
nia. The United States was seriously short of rubber and defense examinations and would you share some
owing to the war with Japan. This project had priority of your experiences?
over the military. My statistical knowledge obtained at Federer: The thing I remember most about my
CSU and my year at ISU was put to the test here as qualifying examination is that I really messed up my
I was known as the statistician on the project. I helped explanation of likelihood ratio procedures. Professor
design experiments, sampling procedures in laborato- Alexander Mood, chairman of my graduate commit-
ries and quality control procedures in a rubber factory. tee, was forgiving and passed me anyway. For the nextA CONVERSATION WITH WALTER T. FEDERER 305
three weeks I sat down to prove that I did know some- Black Diamond train from Buffalo. Cayuga Lake was
thing about likelihood ratio tests, and the effort resulted frozen over for a long distance and the temperature was
in my 12th paper published in 1951 (Federer, 1951). subzero. Dr. Love considered the wife to be an impor-
The defense for my Ph.D. dissertation was mired tant part of hiring an individual as they needed to fit
in departmental politics. Professor Oscar Kempthorne in with the individuals in the department. After a week
wanted me to select him as the chairman of my com- of interviews, Dr. Love offered me an associate profes-
mittee. I wrote two papers (Kempthorne and Federer, sor position at $5,800 per year. Since I wasn’t certain
1948a, b) with him as a peace offering. Also, he was that I wanted to come to Cornell, I didn’t accept right
critical of several major and minor students’ theses. away and then Dr. Love raised the ante to a profes-
Professor Paul Homeyer and I helped a number of sta- sorship at $6,300. I still didn’t give him my answer as
tistics minors through their difficulty. Professor George my wife Lillian wasn’t certain she wanted to leave her
Snedecor, who was a member of my committee, sent Iowa home. As is obvious, we did accept the offer and
Professor Kempthorne in his place for the oral defense came to Cornell in August 1948.
of my Ph.D. dissertation. This was quite an experi- Hedayat: How come you never left Cornell Uni-
ence. My thesis topic was selected and the research versity?
started when Professor W. G. Cochran was chairman Federer: The main reason I never left is Cornell
of my committee. Professor Mood took over as chair- University’s policy of “Freedom with Responsibility.”
man when Professor Cochran moved to North Carolina This fits my nature very well. Dr. Love was unique in
State University. hiring members of his department; he hired leaders and
Hedayat: When did you meet Professor Ronald A. not assistants to a leader. He didn’t believe in “Der Herr
Fisher in person and what were your statistical conver- Professor” mentality. He was very successful at hiring
sations? leaders as exhibited by the positions filled by the group
Federer: While visiting at ISU in the summer of he hired, for example, university president, deans of the
1952, I had the opportunity to meet with Professor faculty, directors of organizations, et cetera. At Cornell
Ronald A. Fisher. Professor Theodore A. Bancroft, University, a person could do just about any kind of
Head of the Stat Lab, arranged to have the graduate research desired, but one CANNOT make anyone else
students meet with the Great Man. During the meeting, join them in an effort. Cooperation can be sought, but
I asked Professor Fisher, “If you were a young statisti- can’t be forced. This policy allowed me to develop
cian who had just received a Ph.D., what line of statis- my statistical research in whatever direction I liked.
tical research would you pursue today?” He stroked his Of course, the grants obtained do determine the direc-
beard and after a few minutes said, “Ah yes, if I were tion, but grant areas that conform to one’s goals may
just starting my research career, I would work on se- be selected. When confronted with the opportunity to
quential experimentation. That Abraham Wald did an go elsewhere, I sat down and made a list of the pos-
ingenious thing with his work on sequential sampling.” itives and negatives of Cornell versus another place.
I find his statement interesting because he could make Cornell always won. The sabbaticals (Hawaiian Sugar
the same remark today, as little has been done in this Planters Association and Pineapple Research Institute
area. We don’t know enough to write a Snedecor and in Hawaii, 1954–1955; Mathematical Research Center,
Cochran book based on sequential experimentation and University of Wisconsin, 1962–1963 and 1969–1970;
methods. I have heard several interesting stories about Sydney University, 1977 and 1984) and visits to other
Professor Fisher, but perhaps this is not the place to
universities in summers let me have the opportunity to
recount them.
compare other places with Cornell. Cornell is, and has
been, a great place to pursue my goals.
STATISTICS AT CORNELL
Hedayat: Cornell University is a combination of
Hedayat: How did you land at Cornell University? a private university and a land-grant college. Has this
Federer: Dr. Harry H. Love (Head of the Depart- been a beneficial arrangement for statistics at Cornell?
ment of Plant Breeding, Cornell University) came to Federer: Cornell has research endeavors in many
ISU to interview individuals for a position as a sta- fields, many of which require statistical applications
tistician. I was invited to visit Cornell University in and statistical research for new procedures for planning
February 1948. My wife, Lillian, and I took the train experiments and analyzing data from research activi-
from Ames, Iowa, to Ithaca, New York, arriving on the ties. This has led to the various Schools and Colleges306 A. S. HEDAYAT
of Cornell hiring statisticians in subject matter depart- as strong, or nearly so, in the mathematical aspects of
ments. This wide dispersion of statisticians at Cornell statistics today as we were in the sixties. It is difficult
has resulted in there being many more statisticians at to make this comparison. It is like comparing apples
Cornell than there would have been in a single statis- with oranges.
tics department. The Departments of Animal Science Hedayat: When I was a graduate student in sta-
and Economics have several statisticians on their pay- tistics at Cornell in the late sixties, my statistics pro-
roll. Several other departments have hired statisticians. fessors included Jacob Wolfowitz, Jack Kiefer, Larry
Thus the private and land grant arrangement has been Brown, Roger Farrell, Harry Kesten, Robert Bechoffer,
beneficial for statistics. Lionel Weiss, Philip McCarthy, Shayle Searle, Douglas
Hedayat: When was a statistics department Robson, yourself and others. Who are the counterparts
founded at Cornell? Why did it take so long to do this? of these individuals?
Federer: The Statistics Center at Cornell was es- Federer: Many of these individuals cannot be re-
tablished in the late forties. The Department of Math- placed as they are one of a kind. For the most part, they
ematics has appointed a number of statisticians and have no counterparts. As I said in the previous state-
probabilists from the thirties up to the present, as for ment, comparisons of then and now are difficult. The
example, John Curtis, Marc Kac, Will Feller, Jacob direction and flavor of statistics is different today than
(Jack) Wolfowitz, Jack Kiefer, Roger Farrell, Larry it was in the sixties.
Brown, Eugene Dynkin, Gene Hwang and Richard Hedayat: You were head of the Biometrics Unit
Durrett, among others. A number of statisticians (Pete for 33 years. What role does a competent staff play in
Morton and Philip McCarthy, for example) held posi- the success of a department?
tions in the School of Industrial and Labor Relations Federer: During the late forties, fifties, sixties and
beginning in the mid-forties. The Biometrics Unit was the seventies, the stenographers in the Biometrics Unit
formed in 1948. It functioned as a department from were known as among the best or the best statisti-
1952 onward. The name of the Plant Breeding Depart- cal and mathematical typists on the Cornell campus.
ment was changed to the Department of Plant Breeding There were no such things as personal computers and
and Biometry in 1966. Statisticians were appointed in word processing packages in the forties and fifties.
the Operations Research Department beginning in the A stenographer was necessary to carry on the teaching
early fifties (e.g., Robert Bechoffer and Lionel Weiss). and research activities of a department. The faculty re-
Professor G. W. Salisbury was in the department of An- lied heavily on a proficient secretarial staff. During the
imal Breeding in the forties and Professor Charles R. early period, I hired wives of Cornell students. These
Henderson was hired in 1948. Over the years, Cornell were extremely bright and competent individuals quick
statisticians talked about a single department beginning to acquire proficiency in mathematical typing. Such in-
in the forties, but it was all talk as individuals did not dividuals as Annabelle Pedersen, Helen Resnick and
want to give up what they presently had and the var- Nola Weed were outstanding. Later on career stenog-
ious school and college deans did not want to let go raphers were hired. Donna VanOrder, Helen Seamon,
of any positions. A Department of Statistical Science Norma Phalen and Pam Archin were among those wor-
came into being in 1997 and a Department of Biomet- thy of mention. These were very capable individuals
rics (now Biological Statistics and Computational Bi- who helped the faculty to pursue their research, teach-
ology) was formed in 1998. ing and consulting activities in an efficient manner.
Hedayat: Is Cornell as strong in statistics as it was Having a competent staff is essential to the success
in the sixties? of any department. Currently, I personally use word
Federer: The research interests of Cornell sta- processing packages such as Word, EXP and Acrobat
tisticians today are different from the sixties. Def- to type my technical reports and papers for publication.
initely, statistical design and sampling were much, Most individuals do this today and the staff of a depart-
much stronger in the sixties than they are today. The ment needs to reflect this change.
J. Kiefer, D. Robson and P. McCarthy research inter-
PAST RESEARCH ACTIVITIES
ests in optimal design, in sampling biological popula-
tions and survey design appear to have disappeared or Hedayat: If you had to select five of your publica-
at least greatly diminished. I believe probability is as tions, what would they be and why?
strong as ever. Biomathematics, modeling, statistical Federer: For me this is a difficult question as there
genetics and other areas are very strong. We may be are nine books and somewhere in the neighborhood ofA CONVERSATION WITH WALTER T. FEDERER 307
300 published papers from which to select. The ones mixtures of crops. Most publications on intercropping,
I select now may be different tomorrow, but here is the growing of more than one crop on the same area of
my selection. The first is my Ph.D. thesis (Federer, land either simultaneously or sequentially, elicit only a
1948), which was a new and innovative method for fraction of the information present in an experiment.
combining the results from a series of experiments These books demonstrate statistical methods for ex-
with different experimental designs and different treat- tracting information from a data set on mixtures. As
ments. My second selection is my first book (Federer, far as I know there are no other books in this area. The
1955) on experimental design. This book was written statistical methods presented have applications in a va-
from a statistical consultant’s viewpoint and contained riety of other fields as explained in Chapter 19 of Vol-
many unusual and different designs and analyses. It ume II.
has been used worldwide and was reprinted by the In- It is possible that a couple of projects I am currently
dian government for many years. My third selection is researching will have significant impact on the statis-
my paper on augmented designs (Federer, 1956). This tical profession. My papers on fractional replication
class of experimental designs was created to replace of factorials and on incomplete block designs are also
the systematic check method in common use by plant candidates for selection. The question asks for individ-
breeders. It is currently in use worldwide and is es- ual works, but my contribution to a topic is usually in
pecially popular outside the United States. This class a series of papers, for example, seven papers on prime-
of experimental designs is useful for screening exper- power lattice designs.
iments where the material to be screened is in short Hedayat: What was the impact of your experi-
supply or the experimenter wishes to limit resources mental design book in comparison with other books at
when screening material. I find considerable satisfac- the same time (Cochran and Cox, 1957; Kempthorne,
tion when something I have created is so widely used 1952)? What was the impact of your other books?
in practice. My fourth selection is a book coauthored Federer: This is a tough question as I find com-
with B. L. Raktoe and A. Hedayat (Raktoe, Hedayat parisons hard to make. My 1955 book is more the-
and Federer, 1981). This publication was selected be- oretical than Cochran and Cox (1957) and less than
cause I feel it is a scholarly and well written work. It is Kempthorne (1952). It is written more from a statisti-
currently out of print. My fifth selection is my 1999 cal consulting point of view than their books. Cochran
book (Federer, 1999). This book together with Vol- and Cox (1957) presents many tables of plans, whereas
ume I (Federer, 1993) represents a new and unique ap- I show how to construct plans and the rationale for us-
proach for designing and analyzing experiments with ing them. Several thousand copies of my book have
F IG . 2. B. Leo Raktoe, Walt Federer and Sam Hedayat at Cornell University, Ithaca, in 1972.308 A. S. HEDAYAT been sold and requests for copies are still being re- of inquiry where mixtures of items are being investi- ceived. Also, permission has been received to trans- gated. Mixtures of items occur in many fields of inves- late the book into an Arabic language. I do not know if tigation such as medicine, manufacturing, marketing, this has been done. The Indian government subsidized recreation, nutrition, and exercise. reprinting the book for many years. To some extent, Hedayat: What do you see as your most important discussion of complexities of split-plot and split-block contributions to statistics? designed experiments are covered in my book, but not Federer: Additional contributions to statistics not in the other two. Papers on this topic have been writ- covered above are presented here. Of course, the de- ten (Federer, 1975, 1977; Federer and Meredith, 1992). velopment of the Biometrics Unit with one faculty Most statisticians even if they know what split-plot and member (me) into a department should be mentioned. split-block designed experiments are, do not realize I was Professor-in-Charge and Director of the Bio- that these designs are not unique to agriculture, but can metrics Unit for 33 years. Whenever I tried to have occur in many fields of investigation. My 1991 book D. S. Robson or S. R. Searle become the administra- (Federer, 1991) is a text for a concept versus a methods tor, they threatened to leave. I am proud of my ability type of course. The statistical profession doesn’t ap- to help and motivate individuals in statistical research. pear to be ready for a book of this type as most are not This was done by obtaining research grants and bring- concerned with how data are collected, but only with ing creative and innovative individuals to work on the what to do with a set of numbers that are considered grants for various lengths of time. These individu- to be data, for example, statistical methods texts. Tech- als were very productive under the climate provided. niques in Chapter 6 could save vast amounts of money For example, in the five-year period preceding 1974, in the analytical laboratories of the world. I think it is 102 papers were published with support from an NIH an excellent book, but that doesn’t make it widely ac- (National Institutes of Health) grant: of these papers, cepted. 18 were in The Annals of Statistics, 12 in Biomet- My two recent books (Federer, 1993, 1999) have the rics and 29 in other statistical journals. Such individ- distinction of having no competitors in the investiga- uals as D. S. Robson, K. S. Banerjee, B. L. Raktoe, tion of mixtures of crops. Their impact is unknown A. Hedayat, Ying Wang, D. Raghavarao, E. Seiden, at this time. The statistical methods developed in the D. A. Anderson, E. T. Parker and others were instru- books could easily be translated to any other field mental in producing this record production of pub- F IG . 3. Walt Federer, Sam Hedayat and D. Raghavarao in Philadelphia attending the 60th birthday conference in honor of Damaraju Raghavarao in 1999.
A CONVERSATION WITH WALTER T. FEDERER 309
F IG . 4. C. R. Rao, Walt Federer, Sam Hedayat and Ed Lakatos attending the 60th birthday conference in honor of Damaraju Raghavarao
in Philadelphia in 1999.
lished research papers over the years. It was always have continued as indicated by some of my current re-
my desire to keep the research efforts of the Biomet- search projects, which include:
rics Unit at a very high level. My advice to colleagues
and young appointees was to keep their research pro- – Documentation of the toolkit Gendex, jointly with
duction at a high level, as this is what gets them pro- developer Nam-Ky Nguyen (Design Computing,
motions and offers for jobs. Administrators count the Australia).
number of publications when considering promotions. – Spatial analyses and exploratory model selection
I do have many ideas for research, but usually need for spatially arranged experiments, jointly with Jose
someone with more mathematical competence to help Crossa (CIMMYT, Mexico).
me to solve the associated problems. The above named – Fractional combinatorial treatment design, jointly
individuals and others have been very cooperative and with Damaraju Raghavarao (Temple University).
helpful in this respect. – Complete sets of sum-of-squares orthogonal F
The Biometrics and Statistics Minor program of the
squares of order n with Hosh Pesotan (University
Biometrics Unit has been very successful over the
of Guelph, Canada) and B. Leo Raktoe (Singapore).
years. A large number of the minor students under
D. S. Robson and myself accepted positions as sta- – Mixed model anomalies in computer packages,
tisticians and many were instrumental in pursuing re- jointly with Russell D. Wolfinger (SAS Institute)
search careers which involved statistical applications and Walter Stroup (University of Nebraska).
and theory, for example, S. R. Searle, R. C. Elston, – Fourier versus polynomial regression for field exper-
D. A. Harville, R. S. Dunbar, M. Grosslein, R. L. Hurst, iments, jointly with Murari Singh (ICARDA, Syria).
G. V. O’Bleness, H. Regier, P. M. Dixon and others. – Construction and analyses for augmented lattice
square experiment designs.
CURRENT RESEARCH ACTIVITIES – The two formulations for variance components for
Hedayat: It is clear that you really have not re- mixed models, jointly with Kaye E. Basford (Uni-
tired. What are you working on now? versity of Queensland, Australia).
Federer: It is true that I have retired only from ad- – Application of the Kalman filter for statistical analy-
ministration, meetings and teaching, but not from sta- ses, jointly with B. R. Murty (Indian Agricultural In-
tistical research and consulting. My research activities stitute).310 A. S. HEDAYAT
Hedayat: You are working on so many different Federer: Doug Robson is the kind of person who
topics with so many different people. How do you find influences anyone with whom he comes in contact.
the time and energy to do all this? When he first arrived at Cornell in 1949, I asked him
Federer: When one has colleagues who are very to review a book on sampling. He found the book to
capable and willing to cooperate, it is relatively easy be about one-third correct. He gave a seminar on a
to have several projects going on at the same time. paper in The Annals of Mathematical Statistics. He
I am near my limit now. I seemed to be blessed with found the paper to be mostly nonsense. Professor Jacob
the ability to have several things going simultaneously Wolfowitz was infuriated by the fact that such a pa-
rather than doing only one project at a time. Also, per would ever be published, let alone in the Annals.
I sometimes feel the energy and enthusiasm of my co- When I nominated him for a Cornell University Grad-
operators. I have been blessed with a very inquisitive uate Fellowship, I was told that the committee said,
mind and really want to know the answers. This cre- “Give Robson a fellowship. Now let us look at the other
ates a driving force within me to know more. candidates.” Interaction with Doug was such a joy as
he could always go right to the nub of a problem and
OTHER COLLEAGUES present it in a clearly understandable manner. He was
Hedayat: Name some people in your life who a great research consultant, and consultees responded
have influenced your statistical thinking. very favorably to him.
Federer: Many people, past and present, have in- Hedayat: Since you are interested in the construc-
fluenced my statistical thinking and direction over the tion of experimental designs, have you or your col-
years. The scientific method has dominated my way leagues discussed Euler’s Latin square conjecture?
of thinking and any scientist who actively pursues Federer: It has always been my hope and thought
these principles has an influence on me. An inquisi- that mathematicians would develop a geometry for all
tive mind is an important trait for a statistician. Also, numbers, something like a single-degree-of-freedom
my elementary school teachers, Miss Butcher and Miss geometry, which would consider all numbers. My de-
Jacque Folck, and high school teachers, Miss Cooper velopment of sum-of-squares orthogonal complete sets
(Latin), Miss King (English), Miss Sweeney (alge- of F squares of order n is a step in this direction.
bra), Miss Ferguson (geometry), Mr. Snow (history) I suspected the Euler conjecture was false and Pro-
and Miss Schwab (social studies), influenced me con- fessor Esther Seiden told me she proved this in the
siderably with their dedicated and scholarly approach late fifties. We wanted to include her original mater-
and activating an inquisitive mind. These people whet- ial in a monograph we coauthored with several other
ted my appetite for knowledge. Aubrey C. Hildreth individuals (Federer et al., 1970). She was unable to
(Director of the Cheyenne Horticultural Research Sta- find her original notes on this when the paper by Bose,
tion), LeRoy Powers (a genius type), Warren Leonard Shrikhande and Parker (1960) appeared, disproving the
(a truly great teacher), Arnold J. King (a very cre- Euler conjecture.
ative individual and excellent administrator), George F.
Sprague (a genius type), George W. Snedecor (an FORCES AND TRENDS IN STATISTICS
excellent teacher), William G. Cochran (a genius
type), Alexander Mood (a great Ph.D. chairman), Hedayat: In the early development of statistics in
Oscar Kempthorne (an experimental design expert), other countries such as England and India, agriculture
Marvin Zelen (an inspiring and creative colleague) and seemed to have been a driving force in its development.
Douglas S. Robson (a genius type) had considerable What are your comments on this?
influence on my statistical thinking. Some other pro- Federer: Agricultural researchers encounter con-
fessors who influenced my thinking patterns were Barr siderable variation in their experimentation. When
(plant physiology, CSU), Johnson (organic chemistry, differences in items of interest, say treatments, are
CSU), Painter (host plant resistance, KSU), DeVries large, variation is less of a concern. When differ-
(German, ISU) and Cooke (modeling, Cornell Univer- ences in treatments become smaller in relation to vari-
sity). There are others but these are the ones I think of ation, this causes concern for the researcher. Hence,
now. a need for better experimental designs and statistical
Hedayat: You list one of your students, Douglas S. methodology was expressed by the early Rothamsted
Robson, as a person who influenced your statistical Experimental Station (England) researchers and ex-
thinking. Do have further comments on this? perimenters elsewhere. This need was answered inA CONVERSATION WITH WALTER T. FEDERER 311
part by such statisticians as Pearson (Karl), Gossett is to be the language of science, much more of sta-
(Student), Fisher, Wishart, Saunders, Yates, Cochran, tistical research needs to be devoted to subject matter
Mahalanobis and Panse. Their research aroused the problems that occur in everyday experimentation rather
interest of many other statisticians and this was very than merely extending or generalizing results of previ-
healthy for the whole of statistics. ous works.
Later on, the need for statistical procedures related to Hedayat: You used the word “pooling” several
product improvement, pharmaceutical, marketing and times in the last question. It reminds me of meta-
medical research were in demand. Demands for better analysis. What are your views on meta-analysis?
statistical methodology supplied the need and, hence, Federer: I consider meta-analysis as a new name
were a driving force for the development of statistical for an older procedure, that is, combining results from
procedures, whether for design or for analysis. experiments. Fisher, Wishart, Cochran, Yates and even
Hedayat: Are you satisfied with current trends in my Ph.D. dissertation considered combining and sum-
statistics? marizing the results from many experiments. There
Federer: In the fifties, I predicted that within was considerable interest among such individuals as
ten years, the major theme at the annual statistics meet- W. G. Cochran and John W. Tukey in preparing a book
ing would be deterministic and stochastic modeling. or monograph on this topic when it was broached. The
It still hasn’t happened. Operations research meetings reason this wasn’t done was probably due to me not
do have presentations on deterministic modeling. I be- pushing it.
lieve that only a small fraction of the material in The Hedayat: Do you appreciate data mining?
Annals of Statistics and The Annals of Probability ever Federer: Data mining, as I understand it, seeks to
gets into practice or into statistics courses. I have some find patterns and explanatory variables in data sets.
Any method that extracts information from a data set is
20 papers in The Annals of Statistics and realize that
useful and is worthy of consideration. I consider some
Annals papers are used mostly to write other papers.
of the investigations I do as data mining. In particular,
I would like to see much more emphasis on sequential
when using exploratory model selection for a spatially
methods and on stochastic modeling in published pa-
designed experiment, I am searching for a model that
pers on statistics. I believe that statistics today is very
fits the spatial pattern present in the experiment. With
weak in the philosophical area. For example, what is
the availability of the computing power we have, data
the nature and meaning of the term error mean square
mining techniques are feasible. I haven’t investigated
and random variation? Measurement theory and phi-
this idea very far, but I believe that statistical design,
losophy are very weak; for example, when is a mea- especially fractional replication, has a role to play in
surement a zero and when a trace, and how does one data mining. A method needs to be devised for finding
score death of a seed versus 100% dormancy? In light the group of parametric vectors that allows estimation
of the advances in computing, I do not consider that of effects for a given data set.
there is an up-to-date text in experimental and treat- Hedayat: What is your view on the development,
ment design or in statistical methodology. I believe role and health of statistical design of experiments?
that the computer can be a great teaching tool, but do Federer: I have no formula for getting statisticians
we really know how to do this? The statistical pro- more interested in statistical design. It is a mystery to
fession is much better in statistical methodology and me how one can make inferences from a set of num-
inference than they are in the planning of experiments. bers when the sampling procedure and the population
I think pooling is an unsung hero of statistics. It enters structure are unknown. Any such inferences can only
statistical procedures in many ways. For example, an have assumed populations and sampling procedures.
error mean square is a pool of several sources of vari- The circular statement “these results apply to the pop-
ation; in hypothesis testing of null and nonnull, there ulation from which the sample was drawn” is used
is a large pool of hypotheses in nonnull; in fractional in statistics classes to support inferences. A statisti-
replication the aliasing structure pools several effects cian gets away with such a vague and often unfounded
together; a pool of effects in a mixture results when statement in the classroom, but the investigator can-
only one response is available; pooling laboratory sam- not as he or she lives in the real world. The results of
ples for analysis can increase efficiency considerably. an investigation usually need to be put into practice.
Despite this widespread appearance of pooling, where I do not believe the statistical profession, in general, is
is it discussed in statistics courses? If statistics really very healthy with respect to statistical design. I have312 A. S. HEDAYAT
always thought that statistical design and sampling MISCELLANEOUS
from populations should be the first courses taught,
Hedayat: Would you list ten courses (topics) that
but all elementary courses I know of start with statis-
tical methods or probability. To me, this is putting the current Ph.D. students in statistics should take?
cart before the horse! Thus statistical design, which in- Federer: As we all know or should know, statistics
cludes a description of the target population, has a vital is (i) the planning and design of investigations, (ii) sta-
role in the teaching of statistics. tistical methodology for summarizing the results of an
With respect to development, many unsolved prob- investigation and (iii) making inferences from the re-
lems remain. These will continue to arise as investi- sults of the investigation to the target population. Any
gations into the unknown continue. New results often curriculum that does not include courses in all three
indicate the need for new methods. A recent book by phases of statistics is deficient. Therefore, courses in
Altan and Singh (2001) indicates the scope of work go- statistical design and survey and laboratory sampling,
ing on and related problems. D. Raghavarao and I have courses in statistical methods, and courses in probabil-
a marketing design that allows estimation of compet- ity and inference should form the core of the curricu-
ing effects of n items in a display. However, we know lum. Of course, a heavy dose of mathematics is also
little or nothing about alternative designs or properties required. The courses should be of the 21st century
of such designs. The field of fractional combinatori- type, making use of available computer technology.
als is in its infancy and requires considerable research I do not know of an up-to-date design of experiments,
to bring this field to the level of fractional replication design of sample surveys and statistical methods text-
of factorials. How much do we know about sequen- book that makes full use of available computer tech-
tial design of experiments? I believe the most needed nology. For example, a statistical design text should
book today is The Planning and Design of Computer have material on computer packages for creating opti-
and Simulation Experiments. I think it will need to be mal or near-optimal statistical designs. Tables of statis-
a joint effort of computer science and statistical design tical designs are inadequate and completely outmoded
experts. In this century, many investigators will want to by available computer software. There is no need to
run a computer experiment or a series of experiments spend time constructing and preparing a randomized
prior to conducting an actual experiment. form of a plan when a package can obtain randomized
Hedayat: What do you think the role and leader- plans in a fraction of a second.
ship of professional statistical societies should be? Hedayat: What is the role of graduate students in
Federer: Professional statistical organizations the success of a department of statistics?
have performed and are performing valuable services Federer: Having competent graduate students is
to the field of statistics through the holding of regional vital to the success of a department. The quality of
and annual meetings. The presentation of invited and
the research in graduate dissertations is a reflection
contributed papers and panel discussions is an incen-
of the department. Having strong minors in biometry
tive to statisticians to do statistical research. They pro-
and statistics reflects very favorably on a department.
vide the statistical advice requested by government
I have been blessed with some very gifted gradu-
agencies. Such programs as Careers in Statistics have
done much to further the cause of statistics. The Amer- ate students such as Douglas S. Robson, Prasert Na
ican Statistical Association has taken on the role of a Nagara, Anne Ebner, G. F. Atkinson, B. Leo Raktoe,
mother organization and has spawned several societies A. Hedayat, John Mandeli, Barbara Grimes, Ronald
and journals that meet the needs of the statistical pro- Kershner, Anila Wijesinha, M. Shafiq and U. B. Paik.
fession. I believe they have met and are meeting the I consider their dissertations outstanding even if some
needs of the statistical community. never continued their research efforts after leaving
Hedayat: Your visibility has been mostly through Cornell. Douglas S. Robson chaired more majors and
research and less so through administrative contribu- minors than I did. The three of us, Robson, Searle and
tions. How far has that been a deliberate choice? myself, were committee members of many students
Federer: Research has been a definite choice on minoring in biometry and statistics. Many of these
my part. In fact, when I was appointed Professor at went on to become full-fledged statisticians.
Cornell University, I asked for and received a letter sta- Graduate students and support of graduate students
ting that half of my time could be devoted to research. is a necessity for the efficient functioning of a depart-
After my appointment, I found out that half time meant ment of statistics. Teaching and research assistantships
evenings and weekends! are a necessity. They afford a competitive advantageA CONVERSATION WITH WALTER T. FEDERER 313
in attracting students into the graduate program. Grad- Hedayat: You have written a few books. What are
uate students are very efficient costwise and they can some of your thoughts on writing books?
perform many technical functions that would otherwise Federer: I find it fun to write papers, but a weari-
have to be performed by high-paid faculty. Administra- some, tedious and time-consuming task to write a
tors who do not appreciate these facts need to be con- book. My first book in 1955 took me approximately
vinced. four years to complete. When I was at the Pineapple
Hedayat: Some of our eminent statisticians have Research Institute in Honolulu in 1954–1955, one of
passed on. Would you wish to comment on a few you the staff asked me how much money I expected to re-
have known? ceive from my book. I gave her a number and then she
Federer: In my mind, Sir Ronald A. Fisher is the asked me how long it took me to write the book and
greatest statistician of our times. His creativity and I gave her a number. She then said, “Oh that would
ability to set the foundations of the statistical field are be $30 an hour. No, $3 an hour. Oh no, three cents an
unparalleled. He covered the entire spectrum in one hour. Heavens, man, you are crazy!” I feel that writ-
way or another. The talk and paper by Savage (1976) ing a scholarly book usually means not much money in
“On rereading R. A. Fisher” stirred a lot of discussion royalties. One usually needs to write a book for enjoy-
of and appreciation for Fisher’s work, even to the pre- ment or for the feeling of accomplishment rather than
sentation at Cornell of a semester course on two of his monetary gain.
papers. A second person who comes to mind is John W. My 1993 book required several years to complete as
Tukey. John was adept in several fields of inquiry. His it was difficult to change my way of thinking from stan-
logic and creativity were marvelous. For his impact on dard statistics to the statistics of mixtures. One of my
the entire statistical profession, George W. Snedecor students, Anila Wijesinha, helped me considerably to
had a very profound effect. Two individuals who had clarify the concepts. It was she who suggested that we
considerable impact on the direction of statistics in do two crops in a mixture before tackling three or more
the United States are Arnold J. King and Gertrude M. crops as I did in Volume II. She decided not to coauthor
Cox through their administrative prowess. Many con- Volume I with me as she had other interests at the time.
veniences statisticians enjoy today are due to such peo- Volume II required an additional four years to prepare
ple as Snedecor, King and Cox. W. Edwards Deming after Volume I was published. Some of the work for
was a remarkable man who had a terrific impact on Volume II had been done in previous years.
manufacturing worldwide. Another person who had The first edition of my 1991 book was written over
considerable impact on the use and usefulness of statis- a period of years for the class “Statistics and the
tical procedures was Frank Yates. Many creative ideas World We Live In.” This course was an artsy statistics
are embedded in his writings. William G. Cochran was course in that statistical concepts rather than statistical
unique among statisticians for his creative and insight- methodologies were emphasized. The second edition
ful approach to solving many problems in statistics. of this book took a year to write.
Even though theoretically well grounded, he could see I have a bit of advice for young professionals who
the usefulness of his research in practice. Chester I. are vying for tenure. Writing a book is very time-
Bliss also comes to mind as a very important figure consuming. This means that if one is writing a book,
in statistics. His dedication and contribution to pro- the number of papers one publishes will be diminished.
cedures for biological analyses were groundbreaking. Since number of publications counts for tenure, one
Of course, when one thinks of this area, the name of should remember that a book is only one publication.
David J. Finney must be mentioned also and as well as It is suggested that book writing be delayed until after
for his many other contributions. Morris Hansen had tenure has been received.
significant and lasting effects on governmental statis-
tics, especially in the Census Bureau. There are nu-
OTHER INTERESTS
merous other individuals whom I knew who have made
significant contributions to our field, but I was told to Hedayat: I know you have many personal interests
limit my selection. Knowing and associating with such beyond statistics. Tell us about them and also tell us
individuals as the aforementioned was a great inspira- whether or not they had any impact on your profession
tion. I have many pleasant memories of associations as a statistician.
with the above as well as with several others who have Federer: Growing up on a small ranch near
passed on. Cheyenne, Wyoming, I did a lot of “cowboying.” I was314 A. S. HEDAYAT
a cattle drover for neighbors from six years old and During consultation, a proposed research project may
on. I “broke” many horses to ride. I never did learn be altered, and many times was. As D. S. Robson and
to ride a bicycle as I was riding horses too much of I have always said, we get many of our research ideas
the time. A model-T Ford was my first car at the age from statistical consultations. I have always considered
of 12. It was purchased for $5 from proceeds of my statistical consulting as the extension part of statistics,
work as a drover. The experiences on the ranch led me that is, extending statistical ideas to scientists. It can
to become a professional rodeo rider for six years. My also be considered as statistical tutoring. Researchers
specialties were bull riding, bareback riding, saddle- are in need of statistical help and having a consulting
bronc riding and the wild horse race. I was a very fre- service available for them is a valuable asset. I believe
quent winner in the last event as I knew how to select that statisticians who do consulting should not consider
a horse that would run and would not spend too much it as a one-way service, but as a two-way valuable ex-
time bucking. I rode in the first college rodeo held at change of information. This raises the value of consult-
CSU in 1936, winning three firsts, three seconds and ing to a higher level than just a service.
the grand field prize. This ended my rodeo days. I did Research is a necessary and important part of any
play football at CSU for three years, wrestled and ran statistics degree program. If the faculty is weak in re-
track. From the time I was a small boy I played base- search efforts, the dissertations will likewise be weak.
ball and later softball, continuing up through my days Turning out poorly qualified graduates reflects badly
at ISU. I played some softball at Cornell. I coached Lit- on a department. Research publication is a neces-
tle League baseball and ice hockey from 1961 to 1970 sity for taking another position. Ordinarily, statisti-
with some first place (also some last place) teams. I al- cal consulting and teaching ability are not sufficient
ways enjoyed dancing of any form. Starting as early conditions, albeit usually necessary, for promotions or
as age 13, I did square dancing, then a lot of ballroom appointment to a position. Publish or perish is almost a
dancing from my high school days up through my Cor- law in the academic world.
nell days. I have danced to a large number of the name
big bands from the thirties through the fifties. About REFERENCES
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me stop in 2001. And then there are golfing, gardening the Conference in Honor of Professor Damaraju Raghavarao.
and skiing. I love downhill skiing, but have settled for Nova Science, Huntington, NY.
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